Numeracy Higher November 2017 Unit 2 Q3
3. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Handmade socks, knitted using pure cashmere wool, are very expensive to buy.
Rowena buys cashmere wool in 20 g balls.
Each ball of cashmere wool costs her £1.42.
She pays her sister £8 to knit each pair of socks.
135 g of cashmere wool is used to knit each pair of socks.
Rowena sells 40 pairs of cashmere socks for £18.95 per pair.
What is her percentage profit?
Give your answer correct to 2 significant figures.
You must show all your working. [7 + 2 OCW]
Rowena’s percentage profit when selling all 40 pairs of socks is …………… %,
correct to 2 significant figures.
| Scheme | Marks | Comments | ||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Accept rounding or truncation of 1/2p throughout | ||||||||||||||||||||||||||||||||
| (Balls of wool per pair) 135 ÷ 20 (× 40) 6.75 (balls) or 7 (balls) or 270 (balls) or 280 (balls) | M1 A1 | |||||||||||||||||||||||||||||||
| (Costs are 40 ×) 1.42 × 135 ÷ 20 (+(40 ×) 8) | m1 | FT 135 ÷ 20 = 6.75 balls and 7 balls
| ||||||||||||||||||||||||||||||
| (Profit = Sales – Costs), e.g. (Profit per pair) 18.95 - 1.42 × 135 ÷ 20 - 8 OR (Profit for 40 pairs) 40 × 18.95 – 40 × (1.42 × 135 ÷ 20 + 8) OR Appropriate amounts used to calculate (100 ×) \(\dfrac{\text{total sales}}{\text{total costs}}\) - 1(× 100) | M2 |
M1 for any 1 of the following:
40 × 18.95 - 40 × (1.42 × 135 ÷ 20)
18.95 – 40 × (1.42 × 135 ÷ 20 + 8) | ||||||||||||||||||||||||||||||
| Use of appropriate amounts to calculate: (Percentage profit = 100 ×) \(\dfrac{\text{profit}}{\text{costs}}\) or (100 ×) \(\dfrac{\text{sales}}{\text{costs}}\) - 1(× 100) | m1 | FT from previous M1 or M2 FT \(\dfrac{18.95 - \textit{‘their cost per pair’}}{\textit{‘their cost per pair’}}\) OR \(\dfrac{\textit{‘40 }\times\textit{ ‘their 18.95’ – ‘their total costs’}}{\textit{‘their total costs’}}\) OR equivalent | ||||||||||||||||||||||||||||||
| 7.8(%) or 5.6(%) | A1 | No other FT, must be 2 s.f. 7.8% CAO comes from use of 6.75 balls, 5.6% CAO comes from use of 7 balls | ||||||||||||||||||||||||||||||
| See below for OCW strands. | ||||||||||||||||||||||||||||||||
| Organisation and communication | OC1 | For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means | ||||||||||||||||||||||||||||||
| Writing | W1 | For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc. | ||||||||||||||||||||||||||||||